Question: Given $ m \angle LOM = 9x + 24$, and $ m \angle MON = 7x + 76$, find $m\angle MON$. $O$ $L$ $N$ $M$
Solution: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {9x + 24} + {7x + 76} = {180}$ Combine like terms: $ 16x + 100 = 180$ Subtract $100$ from both sides: $ 16x = 80$ Divide both sides by $16$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 7({5}) + 76$ Simplify: $ {m\angle MON = 35 + 76}$ So ${m\angle MON = 111}$.